Theorem 3.1 ([1]})  
For any \((\mathbf {a}, \, \mathbf {d})\in {A}^n\) , there exists
an affine lattice \(\mathcal {L}(\mathbf {a}, \, \mathbf {d})\subseteq \mathrm {Harm}^1(M)\) 
such that a canonical harmonic field for \((\mathbf {a}, \, \mathbf {d})\)  exists
if and only if
\(\xi \in \mathcal {L}(\mathbf {a}, \, \mathbf {d})\) 
